1. Field of the Invention
The present invention relates to a rod lens array for line scanning as an optical system for line scanning used in a scanner, printer, or the like.
2. Description of the Related Art
A rod lens array has been used widely as an optical system for line scanning mainly in consideration of cost. The optical system for line scanning is employed in a scanner, a printer that includes an LED array optical system as a light source, or the like. The rod lens array includes a plurality of rod lenses that have a refractive index distribution in the radial direction and are arranged in rows with their optical axes in parallel. In such a case, an overlapping degree m is set while considering the balance between the periodic light quantity irregularity and the resolution, which is given by
m=X0/2r0xe2x80x83xe2x80x83Eq. 10
where r0 is the radius of the rod lens and X0 is the image radius (field of view) that the single rod lens projects onto an image plane. Here, X0 is defined as X0=xe2x88x92r0/cos(Z0xcfx80/P), where Z0 is the length of the rod lens and P is the one-pitch length thereof.
The resolution is degraded with increases in the overlapping degree m and the periodic light quantity irregularity is increased with decreases in that degree. In general, a relatively large overlapping degree m has been adapted in lens design to suppress the periodic light quantity irregularity that causes vertical stripes (streaks) in the sub-scanning direction of an output image. This is because suppression of the periodic light quantity irregularity is the main purpose of the rod lens array design.
A printer using an LED array optical system as a light source corrects the quantity of light from each of the point light sources so as to eliminate the periodic light quantity irregularity of a rod lens array. Also, a scanner performs input correction (shading correction) so as to eliminate the periodic light quantity irregularity of a rod lens array. The progress in digital data processing technology enables these corrections, and thus the periodic light quantity irregularity can be corrected easily by about 10%.
With a steady increase in the resolution of equipment, optical printers are beginning to shift their resolution from 600 dpi to 1200 dpi.
The optical system for line scanning causes a larger periodic light quantity irregularity, compared with an optical system for field scanning used in copiers or the like. Therefore, it is desirable that the overlapping degree m of a rod lens array for line scanning, defined by Equation 10, is set so as to minimize the periodic light quantity irregularity.
The optical system for line scanning may cause the positional deviation of an image line in the sub-scanning direction (i.e., the direction perpendicular to the main scanning direction). Therefore, the design for preventing an increase in the periodic light quantity irregularity due to such positional deviation also is desirable.
Conventionally, the relationship between the overlapping degree m and the periodic light quantity irregularity has been calculated according to a method disclosed in APPLIED OPTICS/Vol. 19, No. 7/1 Apr. 1980, APPLIED OPTICS/Vol. 21, No. 6/15 March 1982, or the like.
However, it is difficult to achieve a rod lens array for line scanning that provides high brightness and resolution when a relatively large overlapping degree m is adapted in the lens design.
Moreover, the methods disclosed in the above documents assume that the light quantity distribution of rod lenses on an image plane is elliptical. This leads to the conclusion that the periodic light quantity irregularity does not change depending on the rod lens arrays having different angular apertures. Here, the angular aperture is a maximum angle of incidence and indicates the range over which the lenses can accept light.
Thus, the above conventional methods cannot determine the range of the overlapping degree m that is not affected by the positional deviation of an image line in the sub-scanning direction for each rod lens array having a different angular aperture.
Therefore, with the foregoing in mind, it is an object of the present invention to provide a rod lens array for line scanning that can provide high brightness and resolution and suppress the periodic light quantity irregularity to less than 10%.
The present invention also has an object of providing a rod lens array for line scanning that can reduce the degradation of image quality (i.e., vertical stripes (streaks) in the sub-scanning direction of an output image) caused by the periodic light quantity irregularity while considering an angular aperture and the positional deviation of an image line in the sub-scanning direction.
A rod lens array for line scanning according to a first configuration of the present invention includes a plurality of rod lenses having a refractive index distribution in the radial direction that are arranged in one row in the main scanning direction with their optical axes in parallel. An overlapping degree m is in the range defined by
(1.55+0.5j)D/dxe2x89xa6mxe2x89xa6(1.80+0.5j)D/dxe2x80x83xe2x80x83Eq. 11
where d is a lens diameter of the rod lenses, D is an array pitch of the rod lenses and j is zero or a positive integer, and the overlapping degree m is given by m=X0/d, where X0 is the image radius that a single rod lens projects onto an image plane.
A rod lens array for line scanning according to a second configuration of the present invention includes a plurality of rod lenses having a refractive index distribution in the radial direction that are arranged in two rows in the main scanning direction with their optical axes in parallel. An overlapping degree m is in the range defined by
(0.90+0.5j)D/dxe2x89xa6mxe2x89xa6(1.08+0.5j)D/dxe2x80x83xe2x80x83Eq. 12
where d is a lens diameter of the rod lenses, D is an array pitch of the rod lenses and j is zero or a positive integer, and the overlapping degree m is given by m=X0/d, where X0 is the image radius that a single rod lens projects onto an image plane.
A rod lens array for line scanning according to a third configuration of the present invention includes a plurality of rod lenses having a refractive index distribution in the radial direction that are arranged in three rows in the main scanning direction with their optical axes in parallel. An overlapping degree m is in the range defined by
(1.30+0.5j)D/dxe2x89xa6mxe2x89xa6(1.60+0.5j)D/dxe2x80x83xe2x80x83Eq. 13
where d is a lens diameter of the rod lenses, D is an array pitch of the rod lenses and j is zero or a positive integer, and the overlapping degree m is given by m=X0/d, where X0 is the image radius that a single rod lens projects onto an image plane.
According to the first, second or third configuration of the rod lens array for line scanning, it is possible to provide a rod lens array for line scanning that can reduce the degradation of image quality (i.e., vertical stripes (streaks) in the sub-scanning direction of an output image) caused by the periodic light quantity irregularity.
A rod lens array for line scanning according to a fourth configuration of the present invention includes a plurality of rod lenses having a refractive index distribution in the radial direction that are arranged in one row in the main scanning direction with their optical axes in parallel. An overlapping degree m is in the ranges defined by
1.57D/dxe2x89xa6mxe2x89xa61.70D/dxe2x80x83xe2x80x83Eq. 14
2.04D/dxe2x89xa6mxe2x89xa62.42D/dxe2x80x83xe2x80x83Eq. 15
where d is a lens diameter of the rod lenses and D is an array pitch of the rod lenses, and the overlapping degree m is given by m=X0/d, where X0 is the image radius that a single rod lens projects onto an image plane.
A rod lens array for line scanning according to a fifth configuration of the present invention includes a plurality of rod lenses having a refractive index distribution in the radial direction that are arranged in an even number of rows of more than one in the main scanning direction with their optical axes in parallel. An overlapping degree m is in the ranges defined by
0.89D/dxe2x89xa6mxe2x89xa60.95D/dxe2x80x83xe2x80x83Eq. 16
1.10D/dxe2x89xa6mxe2x89xa61.28D/dxe2x80x83xe2x80x83Eq. 17
where d is a lens diameter of the rod lenses and D is an array pitch of the rod lenses, and the overlapping degree m is given by m=X0/d, where X0 is the image radius that a single rod lens projects onto an image plane.
A rod lens array for line scanning according to a sixth configuration of the present invention includes a plurality of rod lenses having a refractive index distribution in the radial direction that are arranged in an odd number of rows of more than two in the main scanning direction with their optical axes in parallel. An overlapping degree m is in the ranges defined by
1.44D/dxe2x89xa6mxe2x89xa61.56D/dxe2x80x83xe2x80x83Eq. 18
1.80D/dxe2x89xa6mxe2x89xa62.13D/dxe2x80x83xe2x80x83Eq. 19
where d is a lens diameter of the rod lenses and D is an array pitch of the rod lenses, and the overlapping degree m is given by m=X0/d, where X0 is the image radius that a single rod lens projects onto an image plane.
According to the fourth, fifth, or sixth configuration of the rod lens array for line scanning, it is possible to provide a rod lens array for line scanning that can provide high brightness and resolution and suppress the periodic light quantity irregularity to less than 10%.
These and other advantages of the present invention will become apparent to those skilled in the art upon reading and understanding the following detailed description with reference to the accompanying figures.